The duo, who have both been out of action since December, are unlikely to feature in Wednesday's Capital One Cup semifinal but are on the verge of being available again
Both players trained with the rest of the first-team squad for all but the final part of Tuesday's session at the club's Carrington training base as they near a return to action.
Van Persie has been sidelined for over a month with a thigh injury, with the Netherlands international last featuring for United in the Champions League victory over Shakhtar Donetsk on Dec. 10.
The 30-year-old worked with PSV Eindhoven fitness coach Arno Philips in a bid to step up his recovery, with Goal revealing Van Persie returned to Manchester on Jan. 9 after completing the two weeks of specialist fitness work in Holland.
Former Everton midfielder Fellaini, meanwhile, underwent wrist surgery towards the end of December and, despite initial fears that he could be out of action for six weeks, has recovered ahead of schedule.
It is unlikely that Van Persie or Fellaini, who trained without a cast on his wrist on Tuesday, will be available for Wednesday's Capital One Cup semifinal second leg, with there being only an outside chance that they will be named on the substitutes' bench.